 # D8.A.2.6 Bending

The design bending moment capacity of a section is primarily dependent on whether the member is laterally supported or unsupported.

You can control the lateral support condition of the member by the use of LAT parameter. The type of member (i.e., cantilever, simply supported, or general) is specified using the CAN parameter.

If the member is laterally supported, then the design strength is calculated as per the provisions of the section 8.2.1 of IS 800:2007, based on the following factors:

• Whether section with webs susceptible to shear buckling before yielding
• Ratio of shear force to design shear strength
• Section classification

If the member is laterally unsupported, then the design strength is calculated as per the provisions of the section 8.2.2 of IS 800:2007, based on the following factors:

• Lateral Torsional Buckling
• Section Classification

Laterally unsupported sections of a solid rod are considered as laterally supported as mentioned in Cl. 8.2.2(b). The plastic moment of inertia, Zp, is calculated as D3/6.

## Working Stress Design

Actual bending stress values are given by, about major (Z) and minor (Y) axes, respectively:

 fbcz = Mz/Zecz

 fbtz = Mz/Zetz

 fbcy = My/Zecy

 fbty = My/Zety

The permissible bending stress is given as follows:

1. For laterally supported beams:

• Fabc = Fabt = 0.66·Fy for Plastic or Compact sections
• Fabc = Fabt = 0.60·Fy for Semi-compact sections
where
 Fy = Yield strength of steel, indicated by the FYLD parameter.
2. For laterally unsupported beams:

fabcz = 0.60·Md/Zecz

fabtz = 0.60·Md/Zetz

where
 Md = Design Bending Strength as per Clause 8.2.2 = βb · Zpz · fbd fbd = χLT · Fy / γmo Zez = Elastic Section Modulus of the Section Zpz = Plastic Section Modulus of the Section αLT = 0.21 for Rolled Steel Section and 0.49 for Welded Steel Section βb = 1.0 for Plastic and Compact Section or Zez/Zpz for Semi-Compact Section λLT = Non-dimensional slenderness ratio λLT = (βb · Zpz · Fy / Mcr)1/2 ≤ (1.2 · Zez · Fy / Mcr )1/2 ϕLT = 0.5 · ( 1 + αLT · ( λLT – 0.2 ) + λLT 2) χLT = The Bending Stress Reduction Factor to account for Lateral Torsional Buckling χLTZ = $1 ϕ L T Z + ϕ L T Z 2 − λ L T Z 2$ Zecz = Elastic Section Modulus of the section about Major Axis for the compression side Zetz = Elastic Section Modulus of the section about Major Axis for the tension side Mcr = $M c r = π 2 E I y L L T 2 ( G I t + π 2 E I w L L T 2 )$ Iy = Moment of inertia about the minor axis LLT = Effective length for lateral torsional buckling as determined using either the KX or LX parameters It = Torsional constant of the section It = Warping constant of the section G = Shear modulus of the material
2. About the minor axis, the permissible bending stress is calculated as for a laterally supported section.

## Slender Sections

For member with slender section subjected to bending, moment is taken by flanges alone. Design bending strength should be calculated with effective elastic modulus disregarding the contribution of web of the section.

 Zez = 2·[Bf · tf 3/12 + (Bf · tf) · (D/2 - tf/2)2 )] ⁄ (0.5 · D)

 Zey = 2·(Bf · tf 3/12) ⁄ (0.5 · Bf)

Where:

where
 Zez = Elastic Section modulus about major principal axis Zey = Elastic Section modulus about minor principal axis Bf = Width of flange Tf = thickness of flange D = Overall depth of section

The Moment Capacity will be Md = Ze· fym0 for "Laterally Supported" condition.

The Moment Capacity will be Md = Ze· fbdm0 for "Laterally Un-Supported" condition.

Where, fbd is defined in clause 8.2.2 of IS:800-2007 (described in previous Working Stress Design section).

Note: Slender section can only attain elastic moment capacity and cannot reach to plastic moment capacity.